1. Field of the Invention
This invention relates to a solid laser. This invention particularly relates to a solid laser, wherein an etalon is located in a resonator in order to bring an oscillation mode to a single longitudinal mode.
2. Description of the Related Art
Various solid lasers, which utilize a solid laser medium doped with neodymium (Nd) and produce a laser beam having a wavelength of a 1 xcexcm band (ranging from approximately 1.0 xcexcm to 1.1 xcexcm), have heretofore been proposed. Examples of the solid laser media doped with neodymium (Nd) include Nd:YVO4, Nd:YAG (Y3Al5O12), Nd:YLF (YLiF4), Nd:GdVO4, Nd:YAlO (YAlO3), and Nd:glass. In the solid lasers of such types, a technique is utilized broadly, wherein a Fabry-Pxc3xa9rot type of etalon is located within a resonator in order to bring an oscillation mode to a single longitudinal mode. The solid lasers utilizing the technique described above are described in, for example, Japanese Unexamined Patent Publication Nos. 5(1993)-218556 and 6(1994)-130328, and 7(1995)-263785. (In this specification, the term xe2x80x9cetalonxe2x80x9d means the Fabry-Pxc3xa9rot type of etalon.)
However, in the conventional single-longitudinal-mode solid lasers, wherein the oscillation mode is brought to the single longitudinal mode by the utilization of the etalon, conditions of the etalon (i.e., the thickness of the etalon, the reflectivity of the etalon, and the inclination of the etalon) and conditions of the resonator (i.e., resonator longitudinal mode intervals), under which good single longitudinal mode characteristics are capable of being obtained, were not clear. Therefore, the problems occur in that, in cases where an etalon, which yields good single longitudinal mode characteristics when being located within a certain resonator, is utilized directly in a different resonator, good single longitudinal mode characteristics cannot be obtained.
Also, the problems occur in that, though good single longitudinal mode characteristics are capable of being obtained, a beam profile becomes bad, and the output becomes low. Thus the conditions of the etalon and the resonator, which simultaneously satisfy the requirements for the single longitudinal mode characteristics, the beam profile, and the output, were not clear.
The inventors conducted extensive research and found that, in cases where each of the thickness of the etalon, the reflectivity of the etalon, and the inclination of the etalon is set at a large value, the single longitudinal mode characteristics become good, but the beam profile becomes bad, and the output becomes low. Also, it was found that, in cases where each of the thickness of the etalon, the reflectivity of the etalon, and the inclination of the etalon is set at a small value, the beam profile becomes good, the output becomes high, but the single longitudinal mode characteristics become bad.
Further, it was found that, in cases where a resonator length is set at a large value (i.e., the resonator longitudinal mode intervals are set to be small), the single longitudinal mode characteristics become bad. Furthermore, it was found that, in cases where the resonator length is set at a small value, the single longitudinal mode characteristics become good, and the beam profile and the output are not much affected by the resonator length.
As for a solid laser, which utilizes Nd:YAG as a solid laser medium and produces a laser beam having a wavelength of a 0.9 xcexcm band, the inventors have already found the conditions of the etalon, under which good, reliable single longitudinal mode characteristics, a good beam profile, and a high output are capable of being obtained simultaneously. The conditions of the etalon are disclosed in Japanese Unexamined Patent Publication No. 8(1996)-186316. However, as for the solid laser, which produces a laser beam having a wavelength of the 1 xcexcm band, appropriate conditions of the etalon have not yet been clarified.
The primary object of the present invention is to provide a single-longitudinal-mode solid laser, which produces a laser beam having a wavelength of a 1 xcexcm band and which exhibits good, reliable single longitudinal mode characteristics, a good beam profile, and a high output.
The present invention provides a single-longitudinal-mode solid laser capable of producing a laser beam having a wavelength of a 1 xcexcm band, the solid laser comprising:
i) a solid laser medium doped with neodymium,
ii) a resonator, and
iii) a Fabry-Pxc3xa9rot type of etalon, which is located within the resonator and brings an oscillation mode to a single longitudinal mode,
wherein a thickness of the etalon, a reflectivity of the etalon, an inclination of the etalon, and a resonator longitudinal mode interval are adjusted so as to satisfy the relationships represented by the formulas:
1.2%xe2x89xa6RNxe2x89xa615% and 0.5xc2x0xe2x89xa6xcex8xe2x89xa62.0xc2x0
in which RN represents an effective reflectivity of the etalon with respect to wavelengths xcex=xcex0xc2x1xcex94xcexc deviating by a resonator longitudinal mode interval xcex94xcexc from a resonance wavelength xcex0 of the etalon, and xcex8 represents an inclination of an optical axis of the etalon with respect to an optical axis of the resonator.
The single-longitudinal-mode solid laser in accordance with the present invention should preferably be modified such that the thickness of the etalon, the reflectivity of the etalon, the inclination of the etalon, and the resonator longitudinal mode interval are adjusted so as to satisfy the relationships represented by the formulas:
3.0%xe2x89xa6RNxe2x89xa610% and 0.80xc2x0xe2x89xa6xcex8xe2x89xa61.5xc2x0
in which RN represents the effective reflectivity of the etalon, and xcex8 represents the inclination of the optical axis of the etalon with respect to the optical axis of the resonator.
Effects of the single-longitudinal-mode solid laser in accordance with the present invention will be described hereinbelow.
The Fabry-Pxc3xa9rot type of etalon is a wavelength selecting device utilizing multiple interference of light. FIG. 3 is a graph showing relationships among an effective reflectivity of an etalon, an etalon longitudinal mode, and a resonator longitudinal mode. In FIG. 3, a curve xe2x80x9caxe2x80x9d indicates the wavelength characteristics of an effective reflectivity Reff of the etalon. As illustrated in FIG. 3, the effective reflectivity Reff of the etalon changes periodically, and the etalon longitudinal mode occurs at points, at which the effective reflectivity Reff becomes equal to 0 at a wavelength interval xcex94xcexe (FSR: free spectral range).
In FIG. 3, a curve xe2x80x9cbxe2x80x9d indicates a gain spectrum of a solid laser medium. Ordinarily, the resonator longitudinal mode occurs at a plurality of points falling within an oscillation wavelength width W in the gain spectrum. Therefore, in cases where the etalon is not utilized, the laser undergoes oscillation in a multiple longitudinal mode. In cases where the etalon is inserted into the resonator, the loss, to which each of the longitudinal modes of the resonator is subjected, is modulated in accordance with the effective reflectivity Reff of the etalon. Also, oscillation occurs only in the mode, which is subjected to the smallest loss among the plurality of the resonator longitudinal modes falling within the wavelength width W.
In the manner described above, with the etalon, the oscillation mode is brought to the single longitudinal mode. However, heretofore, it was not clear how the loss modulation with the effective reflectivity Reff of the etalon and the inclination of the etalon are to be set in order for all of the three requirements with respect to good, reliable single longitudinal mode characteristics, a good beam profile, and a high output to be satisfied.
The inventors conducted extensive research in order to clarify how the loss modulation with the effective reflectivity Reff of the etalon and the inclination of the etalon are to be set in order for all of the three requirements with respect to good, reliable single longitudinal mode characteristics, a good beam profile, and a high output to be satisfied. It was thus found that all of the three requirements described above are capable of being satisfied in cases where appropriate loss modulation is given by setting the effective reflectivity RN of the etalon with respect to the wavelengths xcex=xcex0xc2x1xcex94xcexc deviating by the resonator longitudinal mode interval xcex94xcexc from the resonance wavelength xcex0 of the etalon (as illustrated in FIG. 3) so as to fall within a specific range, and in cases where the inclination xcex8 of the optical axis of the etalon is also set so as to fall within a specific range. As described above, the specific range of the effective reflectivity RN of the etalon is represented by the formula 1.2%xe2x89xa6RNxe2x89xa615%, and should preferably be represented by the formula 3.0%xe2x89xa6RNxe2x89xa610%. Also, the specific range of the inclination xcex8 of the optical axis of the etalon is represented by the formula 0.5xc2x0xe2x89xa6xcex8xe2x89xa62.0xc2x0, and should preferably be represented by the formula 0.8xc2x0xe2x89xa6xcex8xe2x89xa61.5xc2x0.
How the effective reflectivity RN of the etalon is calculated will be described hereinbelow. Firstly, ordinarily, in accordance with Airy""s Formulae, the effective reflectivity Reff of the etalon may be represented by Formula (1) shown below.                                                                         R                eff                            =                              xe2x80x83                            ⁢                                                F                  ⁢                                      xe2x80x83                                    ⁢                                                            sin                      2                                        ⁡                                          (                                              δ                        /                        2                                            )                                                                                        1                  +                                      F                    ⁢                                          xe2x80x83                                        ⁢                                                                  sin                        2                                            ⁡                                              (                                                  δ                          /                          2                                                )                                                                                                                                                                                    xe2x80x83                            ⁢                              F                =                                                      4                    ⁢                    R                                                                              (                                              1                        -                        R                                            )                                        2                                                                                                                                          xe2x80x83                            ⁢                              δ                =                                                      4                    ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                                          n                      e                                        ⁢                                          l                      e                                                        λ                                                                                        (        1        )            
wherein R represents the coating reflectivity of the etalon, ne represents the refractive index of the etalon, le represents the thickness of the etalon, and represents the wavelength of light.
Also, the longitudinal mode interval xcex94xcexe of the etalon may be represented by Formula (2) shown below.
xcex94xcexe=xcex02/(2nele)xe2x80x83xe2x80x83(2) 
wherein xcex0 represents the oscillation wavelength of the etalon.
Thereafter, the resonator longitudinal mode interval xcex94xcexc is calculated in the manner described below. In cases where media (including air) respectively having refractive indexes of n1, n2, n3, n4, . . . stand side by side within the resonator, and the thicknesses of the media are respectively l1, l2, l3, l4, . . . , a resonator optical path length Lopt may be represented by Formula (3) shown below.                               L                      o            ⁢                          xe2x80x83                        ⁢            p            ⁢                          xe2x80x83                        ⁢            t                          =                              ∑            i                    ⁢                                    n              i                        ⁢                          l              i                                                          (        3        )            
Therefore, the resonator longitudinal mode interval xcex94xcexc may be represented by Formula (4) shown below.
xcex94xcexc=xcex02/2Loptxe2x80x83xe2x80x83(4) 
From Formulas (1), (2), and (4) shown above, the effective reflectivity RN of the etalon with respect to the wavelengths xcex=xcex0xc2x1xcex94xcexc deviating by the resonator longitudinal mode interval xcex94xcexc from the resonance wavelength xcex0 of the etalon may be approximately represented by Formula (5) shown below.                                                                         R                N                            =                              xe2x80x83                            ⁢                                                F                  ⁢                                      xe2x80x83                                    ⁢                                                            sin                      2                                        ⁡                                          (                                                                        δ                          N                                                /                        2                                            )                                                                                        1                  +                                      F                    ⁢                                          xe2x80x83                                        ⁢                                                                  sin                        2                                            ⁡                                              (                                                                              δ                            N                                                    /                          2                                                )                                                                                                                                                                                    xe2x80x83                            ⁢                                                δ                  N                                =                                                                            Δ                      ⁢                                              xe2x80x83                                            ⁢                      λ                      ⁢                                              xe2x80x83                                            ⁢                      c                                                              Δ                      ⁢                                              xe2x80x83                                            ⁢                      λ                      ⁢                                              xe2x80x83                                            ⁢                      e                                                        xc3x97                  2                  ⁢                                      xe2x80x83                                    ⁢                  π                                                                                        (        5        )            
Bases for the value ranges of the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon described above will hereinbelow be described in detail.
(a) Single Longitudinal Mode Characteristics
In the solid laser, in which the oscillation mode is brought to the single longitudinal mode by the utilization of the Fabry-Pxc3xa9rot type of etalon, the resonator temperature is successively changed by 10xc2x0 C., and the rate of the temperature region, in which the oscillation occurs in the single longitudinal mode, is calculated in units of %. The thus calculated rate of the temperature region is taken as an index for the single longitudinal mode characteristics. Basically, the index for the single longitudinal mode characteristics changes as illustrated in FIG. 4 in accordance with the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon.
(b) Output
The laser output, which is obtained when an etalon provided with an anti-reflection (AR) coating layer (RN=0) is inserted into the resonator at an etalon inclination xcex8 approximately equal to 0xc2x0, is taken as 100%. Also, the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon are set at various values, and the laser outputs are measured. The ratios of the thus measured laser outputs to the aforesaid laser output taken as 100% were calculated. FIG. 5 shows how the ratio of the measured laser output changes in accordance with the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon. In the determination of the characteristics, the resonator length was kept at a predetermined value.
(c) Beam Quality
Basically, the beam quality, expressed in terms of the M2 value, changes as illustrated in FIG. 6 in accordance with the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon. In the determination of the characteristics, the resonator length was kept at a predetermined value.
From the characteristics shown in FIGS. 4, 5, and 6, it is capable of being known in what ranges the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon are to be set with respect to arbitrary specifications concerning the single longitudinal mode characteristics, the output, and the beam quality. For example, comparatively loose specifications as shown below:
Single longitudinal mode characteristicsxe2x89xa780%
Outputxe2x89xa730%
M2xe2x89xa61.2
are capable of being accomplished in cases where the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon are set so as to fall within the range hatched in FIG. 7. In such cases, 1.2%xe2x89xa6RNxe2x89xa615% and 0.5xc2x0xe2x89xa6xcex8xe2x89xa62.0xc2x0.
Also, for example, comparatively strict specifications as shown below:
Single longitudinal mode characteristicsxe2x89xa7100%
Outputxe2x89xa750%
M2xe2x89xa61.05
are capable of being accomplished in cases where the effective reflectivity RN of the etalon and the inclination xcex8 of the optical axis of the etalon are set so as to fall within the range hatched in FIG. 8. In such cases, 3.0%xe2x89xa6RNxe2x89xa610% and 0.8xc2x0xe2x89xa6xcex8xe2x89xa61.5xc2x0.